A Novel Inter-Porosity Flow Model for Multi-Scale Shale Reservoirs with Nonuniform Laminated Fractures

Abstract

Abstract In shale reservoirs, the presence of nano-scale pores and natural fractures leads to various phenomena, such as micro-scale effects and media deformation. Further studies are necessary to better understand the flow mechanisms occurring within nanopores and micro-fractures. Moreover, the flow relationship among organic pores, inorganic pores, and laminated fractures is not well understood and the existing methods for evaluating shale oil productivity do not adequately account for the heterogeneous distribution of laminated fractures. Therefore, the primary objective of this paper is to develop a comprehensive mathematical model that encompasses multi-scale and multi-mechanism coupled flow for shale oil reservoirs, with a specific emphasis on characterizing the inter-porosity flow occurring between different media. The apparent permeability model has been established coupling adsorption, slip, and stress sensitivity characteristics of matrix. By utilizing fractal theory, the non-uniform characteristics of aperture, density, and tortuosity in laminated fractures have been characterized, and finally, an inter-porosity flow model that is applicable to stress-sensitive multi-porosity media has been developed. The accuracy of the model is validated using numerical solution and actual production data with excellent agreement. Notably, the semi-analytical model significantly reduces the computation time. The study investigates the permeability loss of multi-porosity media during production. The results show that the permeability loss of matrix is less than 4%, and that laminated fractures exhibit a significant permeability loss around 30%, while hydraulic fractures suffer a substantial permeability loss exceeding 90%. Oil production varies across media and the contribution of laminated fractures to oil production can reach as high as 80%. Analysis of the heterogeneity of laminated fractures indicates that fractal dimension has a significant effect on the density, aperture, and tortuosity, especially near hydraulic fractures, where density and aperture decrease rapidly with distance. Sensitivity analysis has shown that longer hydraulic fracture can make the single well maintain higher production for a long time.